Assessment of Different Mathematical Models for Analysis of Low-Velocity Impact on Composite Plates in Presence of Pre-loads

In this paper, the low-velocity impact response of composite plates in the presence of pre-loads is investigated using three new models for contact force estimation. The boundary conditions are considered as simply supported and the behavior of the material is linear elastic. The equations are based on both classical and first order shear deformation theory and the Fourier series method is used to solve the governing equations. The mass of the impactor is considered to be large mass and therefore the impact response is categorized as quasi-static. In the first impact model, the contact force history is first considered as a half-sine and then the maximum contact force and contact duration are calculated.  In the second model, an improved two degree of freedom (ITDOF) spring-mass system is expressed by calculating the effective contact stiffness using a fast-iterative scheme. In the third model, which is expressed for the first time in this paper, the plate is considered as a series of masses and springs constructing a multi degree of freedom (MDOF) spring-mass system and the average forces applied to springs is introduced as the contact force. Validation of these models is done by comparing the results with the analytical, numerical and experimental results and shows good agreement. Results show that the new MDOF spring-mass system is more accurate for calculating the contact force rather than the ITDOF spring-mass system.